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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Delta-structures on mapping class groups and braid groups


Authors: A. J. Berrick, E. Hanbury and J. Wu
Journal: Trans. Amer. Math. Soc. 366 (2014), 1879-1903
MSC (2010): Primary 20F36; Secondary 55Q40, 55R80, 55U10, 57M07, 57S05
Published electronically: November 25, 2013
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Abstract: We describe a Delta-group structure on the mapping class groups of surfaces, and show that it is compatible with the Delta-group structures of the braid groups of surfaces given by Berrick-Cohen-Wong-Wu. We then prove an isomorphism theorem relating these two Delta-groups. This is the first of a pair of papers on this topic.


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Additional Information

A. J. Berrick
Affiliation: Department of Mathematics, National University of Singapore, Singapore
Address at time of publication: Yale-NUS College, Singapore 138614, Singapore
Email: berrick@math.nus.edu.sg, berrick@yale-nus.edu.sg

E. Hanbury
Affiliation: Department of Mathematics, Durham University, Durham DH1 3LE, United Kingdom
Email: elizabeth.hanbury@durham.ac.uk

J. Wu
Affiliation: Department of Mathematics, National University of Singapore, Singapore
Email: matwuj@math.nus.edu.sg

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05889-8
PII: S 0002-9947(2013)05889-8
Received by editor(s): January 20, 2012
Received by editor(s) in revised form: May 1, 2012, and May 29, 2012
Published electronically: November 25, 2013
Additional Notes: The authors gratefully acknowledge the assistance of NUS research grants R-146-000-097-112, R-146-000-101-112 and R-146-000-137-112.
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.